In a quality control process, the manager's major concern is to keep the defectives less than 25 per day in order to receive bonus. To make sure this, the manager collected the test data from 12 days. Based on the test data, the sample mean defectives is 21 per day and the sample standard deviation is 12.7 per day. The company cannot afford more than 1% risk in the test. Answer the following questions by using Hypothesis testing method:

a) Based on the data, do you think the manager should receive bonus? Why?

b) There will be a penalty if the number of defectives is over 25. Do you think the manager will get a penalty based on the data? Why?

c) List two major assumptions you have to make in your tests.